States and Properties - TEST Tutorial

(Daemons are sub-divided into these 12 sections. States, the current topic, is the best place to start.)

	Closed Process	Closed Steady	Open Steady
Open Process	Closed Cycle	Open Cycles	States-II
HVAC	Combustion	Equilibrium	Gas Dynamics

(Each section above is divided into two sub-sections - Manual and Applications.)
Manual

(The Manual page complements this Applications page.)

Daemons>States and Properties> Applications

EXAMPLE-1

Calculate the mass of air (in kg and lbm) in a tank of size 6000 ft³. The gas temperature is 20^oC and the pressure is 14.7 psia.

What-if scenario: (a) How would the pressure change if the temperature were gradually increased to 500^oC? (b) Repeat the study for CO₂. Assume ideal gas behavior.

Time Saver: To reproduce the visual solution, copy and paste
this TEST-code on the I/O panel
of the appropriate daemon, click the Load button followed by the Super-Calculate button.

# HOME>Daemons>States>Volume>IdealGas;

States {
             State-1: Air;
             Given:    { p1= 14.7 psia;   T1= 20.0 deg-C;   Vel1= 0.0 m/s;
                               z1= 0.0 m; Vol1= 6000 ft^3;   }
    }

Step 1: Launch
the Volume State daemon.

Solution

To arrive at the appropriate daemon for this state problem, click on Daemons on the Task Bar and then on States, Volume and IdealGas in sequence. Or, use the TEST-Map and jump to the daemon page directly. Note that the Perfect Gas model will produce the same result.

Fig.1.1 Image of the Daemons.States.Volume.IdealGas page. To enter a variable,
click on the checkbox, type in the value and then choose unit. The variables are registered only after you click the Calculate button or press the Enter key.

Step 2: Choose
an ideal gas.

Step 3: Input known
variables.

Step 4: Calculate
the State.

Air is the default gas.

The default State number is State-1. Enter the known variables, thermodynamic properties p1 and T1 and the system property Vol1. Choose appropriate units from the unit selectors.

A Calculate produces the entire state. The system mass, m1, is 204.7 kg. To get the answer in lbm, simply select lbm from the unit selector. The mass is now displayed as 451.3 lbm.

Step 5: A parametric study

To obtain the trend of how pressure changes with temperature, let us calculate three intermediate states between 20^oC and 500^oC. Choose State-5 from the state selector, and enter T5 as 500^o C. Obviously, the mass and volume remain unchanged in this system. Enter m5 as '=m1' and Vol5 as '=Vol1' (do not enter the quotation mark). A Calculate produces the complete State-5 . Now choose State-2 , and enter T2 as '=T1+(T5-T1)/4' , m2 as '=m1' and Vol2 as '=Vol1'. A Calculate produces the complete State-2 . Repeat the same analysis for State-3 , and State-4 with T3 as '=T1+2*(T5-T1)/4' , and '=T1+3*(T5-T1)/4' respectively.

Step 6: Thermodynamic plot.

Step 7: What-if scenarios.

To plot the states on a thermodynamic diagram, say p-T diagram, simply choose p-T from the diagram selector. The graph appears on a separate pop-up window. Volume and mass (hence, density) remaining constant, we expect pressure to vary linearly with temperature. This conclusion is almost trivial from the ideal gas equation of state (p=rho*R*T). However, if the working fluid is a phase-change fluid or a real gas, a manual solution will be tedious, while the TEST solution procedure remains identical irrespective of the working fluid.

Another advantage of a TEST-solution is once a solution is obtained, it is very simple to change parameters at will and pursue any conceivable what-if scenario. For instance, in the above problem, how does the answers change, if the gas were CO2 instead? To answer that question, change the gas to CO2, click the Calculate button (or just press the Enter key) to register the change. Click the Super-Calculate button to propagate the changed information throughout the solution. What if the volume were different? Select State-1, where the volume appears explicitly. Change vol1 to a new value. Enter (or press click Calculate) to register the change. A Super-Calculate completes the new study.

EXAMPLE-2

Evaluate the following states for R-134a and plot them on a T-s diagram. State-1 : T= - 60^oC, saturated vapor; State-2 : 1000 kPa, isentropic to State-1; State-3 : isobaric (constant p) to State-2, saturated vapor; State-4 : isobaric to State-3, saturated liquid; State-5 : isobaric to State-1 and isenthalpic (constant h) to State-4.

What-if scenario: (a) How would the diagram change if the temperature at State-1 were 0^oC instead?

Time Saver: To reproduce the visual solution, copy and paste
this TEST-code on the I/O panel
of the appropriate daemon, click the Load button followed by the Super-Calculate button.

# HOME>Daemons>States>Volume>PhaseChange;

   States {
           State-1: R-134a;
           Given:       { T1= -60.0 deg-C;   x1= 100.0 %;
                  Vel1= 0.0 m/s;   z1= 0.0 m;   }

           State-2: R-134a;
           Given:       { p2= 1000.0 kPa;   s2= "s1" kJ/kg.K;
                  Vel2= 0.0 m/s;   z2= 0.0 m;   }

           State-3: R-134a;
           Given:       { p3= "p2" kPa;   x3= 100.0 %;   Vel3= 0.0 m/s;
                  z3= 0.0 m;   }

           State-4: R-134a;
           Given:       { p4= "p3" kPa;   x4= 0.0 %;   Vel4= 0.0 m/s;
                  z4= 0.0 m;   }

           State-5: R-134a;
                    Given:       { p5= "p1" kPa;   h5= "h4" kJ/kg;
                  Vel5= 0.0 m/s;   z5= 0.0 m;   }
}

Fig.2.1 Image of the pop up window that displays messages as the TEST-Code above
is loaded on the State daemon Daemons>States>PhaseChange.
Super-Calculate automatically closes this window and recreates the visual solution.

Step 1: Launch the R-134 Volume State daemon.

Step.2: Calculate the states.

Step 3: Plot T-s diagram.

Solution

To arrive at the appropriate daemon for this state problem, click on Daemons on the Task Bar and then on States, Volume, and R-134 in sequence. Or use the TEST-Map and jump to the daemon page directly. Note that the corresponding Surface daemon will produce the same answers.

State-1: Choose State-1, enter T1 and x1 (100%). Calculate .

State-2: Choose State-2, enter p2 and s2 ('=s1'). Calculate .

State-3 : Choose State-3, enter p3 ('=p2') and x3 (100%). Calculate .

State-4 Choose State-4, enter p4 ('=p3') and x4 (0%). Calculate .

State-5: Choose State-5, enter p5 ('=p1') and h5 ('=h4'). Calculate .

Choose T-s from the diagram selector. The plot appears on a pop-up window.

Fig.2.2 Image of the T-s diagrams in Ex. 2.

Step 4: What-if scenario.

Simply change T1 (choose State-1, click on the temperature checkbox twice to initialize and then enter the new value) to its new value, Calculate and Super-Calculate . Another way to accomplish the same is to modify the TEST-Code on the I/O panel by changing T1 to its new value, click the Load button, and then Super-Calculate. Choose T-s to plot the updated states.

What if State-2 pressure was given in terms of pressure at State-4? In that case, State-2 cannot be fully evaluated until State-4 is known. After all the known information are entered, a Super-Calculate will propagate the information back and forth among all the stored states.

E XAMPLE-3

Draw a constant pressure line for p=100 kPa for H2O on a T-s diagram.

What-if scenario: How would the line change if the pressure were 1000 kPa?

Time Saver: To reproduce the visual solution, copy and paste
this TEST-code on the I/O panel
of the appropriate daemon, click the Load button followed by the Super-Calculate button.

# HOME>Daemons>States>Volume>PhaseChange;

States {
            State-1: H2O;
            Given:       { p1= 100.0 kPa;   T1= 20.0 deg-C;
                    Vel1= 0.0 m/s;   z1= 0.0 m;   }

            State-2: H2O;
            Given:       { p2= "p1" kPa;   T2= 50.0 deg-C;
                    Vel2= 0.0 m/s;   z2= 0.0 m;   }

            State-3: H2O;
            Given:       { p3= "p1" kPa;   x3= 0.0 %;
                    Vel3= 0.0 m/s;   z3= 0.0 m;   }

            State-4: H2O;
            Given:       { p4= "p1" kPa;   x4= 50.0 %;
                    Vel4= 0.0 m/s;   z4= 0.0 m;   }

         State-5: H2O;
            Given:       { p5= "p1" kPa;   x5= 100.0 %;
                    Vel5= 0.0 m/s;   z5= 0.0 m;   }

            State-6: H2O;
            Given:       { p6= "p1" kPa;   T6= 150.0 deg-C;
                    Vel6= 0.0 m/s;   z6= 0.0 m;   }

            State-7: H2O;
            Given:       { p7= "p1" kPa;   T7= 200.0 deg-C;
                    Vel7= 0.0 m/s;   z7= 0.0 m;   }

            State-8: H2O;
            Given:       { p8= "p1" kPa;   T8= 300.0 deg-C;
                    Vel8= 0.0 m/s;   z8= 0.0 m;   }

            State-9: H2O;
            Given:       { p9= "p1" kPa;   T9= 400.0 deg-C;
                    Vel9= 0.0 m/s;   z9= 0.0 m;   }

            State-10: H2O;
            Given:       { p10= "p1" kPa;   T10= 500.0 deg-C;
                   Vel10= 0.0 m/s;   z10= 0.0 m;   }
}

Step 1: Launch the H2O State Daemon.

Step 2: Determine a reasonable range for temperature.

Step 3: Calculate a series of
States

Step 5.4: Plot a T-s diagram.

Step 5.5: Change p1 and update all calculations.

Solution

Clearly a State problem, arrrive at the appropriate State daemon page, Daemons. States.Volume. PhaseChange using the Child Tables or the TEST-Map. Select H2O as the working fluid.

Before deciding on a range of states to be evaluated, determine the saturation (boiling) temperature of H2O at 100 kPa. Fot that, enter p1=100 kPa, x1=0 %(or any other value between 0% and 100%), and, Calculate . to produce T1=100^oC. Now we calculate the following States.

State-1 : Enter p1 (100 kPa) and T1 (20^oC), Calculate. The daemon calculates the phase as pure liquid as expected.

State-2 : Enter p2 ('=p1')) and T2 (50^oC), Calculate. The daemon calculates the phase as pure liquid as expected.

State-3 : Enter p3 ('=p1')) and x3 (0%), Calculate. The daemon calculates the saturated liquid state.

State-4 : Enter p4 ('=p1')) and x4 (50%), Calculate. The daemon calculates the state for a 50-50 (by mass) two-phase mixture.

State-5 : Enter p5 ('=p1')) and x5 (100%), Calculate. The daemon calculates the saturated vapor state.

State-6 : Use 'More..' on the State-selector to increase the maximum number of allowed states whenever necessary. Enter p6 ('=p1')) and T6 (150^oC), Calculate . The daemon calculates the phase as superheated vapor as expected.

State-7 : Enter p7 ('=p1')) and T7 (200^oC), Calculate. The daemon calculates the phase as superheated vapor as expected.

State-8 : Enter p8 ('=p1')) and T8 (300^oC), Calculate. The daemon calculates the phase as superheated vapor as expected.

State-9 : Enter p9 ('=p1')) and T9 (400^oC), Calculate. The daemon calculates the phase as superheated vapor as expected.

State-10 : Enter p10 ('=p1')) and T10 (500^oC), Calculate. The daemon calculates the phase as superheated vapor as expected.

Choose T-s from the diagram selector. The plot appears on a pop-up window. Note that the compressed or supercooled liquid (states 1, 2 and 3) is treated as saturated liquid at the same temperature in TEST. This introduces slight error, which is generally acceptable under most engineering situations.

To explore the effect of pressure, simply change p1 (=1000 kPa), Calculate to register the change and Super-Calculate to update all calculations. The new T-s diagram shows that the constant pressure line is moved up as pressure is increased. Use the disconnect button to remove the line. Notice that State-6 seems to be out of sequence in the second plot(why?).

Fig. 3.1 T-s plots at 100 kPa and 1000 kPa. Note that after Super-Calculate State-6 became
supercooled water.

EXAMPLE-4

Steam enters a turbine at 1000 kPa, 500 deg-C at a mass flow rate of 2 kg/s. If the velocity is not to exceed 30 m/s, what is the minimum area of the inlet?

What-if scenario: How would the flow velocity change if the inlet temperature were increased to 900 deg-C ?

Time Saver: To reproduce the visual solution, copy and paste
this TEST-code on the I/O panel
of the appropriate daemon, click the Load button followed by the Super-Calculate button.

# HOME>Daemons>States>Surface>PhaseChange;

States {
State-1: H2O;
Given: { p1= 1000.0 kPa; T1= 500.0 deg-C; Vel1= 30.0 m/s;
z1= 0.0 m; mdot1= 2.0 kg/s; }

State-2: H2O;
Given: { p2= "p1" kPa; T2= 900.0 deg-C; z2= 0.0 m;
mdot2= "mdot1" kg/s; A2= "A1" m^2; }
}

Step 1: Launch the H2O State Daemon.

Step 2: Determine State-1 from the given properties.

Step 3: Calculate a second state using the new temperature.

Solution

Clearly a State problem, arrrive at the appropriate State daemon page, Daemons. States. Surface. PhaseChange using the Child Tables or the TEST-Map. Select H2O as the working fluid.

State-1 : Enter p1 (1000 kPa), T1 (500^oC), mdot1 (2 kg/s) and Vel1 (30 m/s), Calculate. The inlet area is found to be 236 cm^2.

State-2 : Enter p2 ('=p1')) and T2 (900^oC), mdot2 ('=mdot1'), A2 ('=A1'). You have to make Vel2 an unknown by unchecking its checkbox. Calculate . The daemon calculates Vel2=45.8 m/s .

EXAMPLE-5

Superheated water vapor flows through a pipe of diameter 10 cm at 1000 kPa, 400 deg-C, and 30 m/s. Determine the flow rate of (a) mass, (b) kinetic energy, (c) stored energy, (d) flow energy, (d) entropy, (e) stored exergy and (f) flow exergy. Use the PC (phase change) model.

What-if scenario: How would the answers change if the vapor were treated as an ideal gas (IG)?

Time Saver: To reproduce the visual solution, copy and paste
this TEST-code on the I/O panel
of the appropriate daemon, click the Load button followed by the Super-Calculate button.

# HOME>Daemons>States>Surface>PhaseChange;

States    {
    State-0: H2O;
    Given:       { p0= 100.0 kPa;   T0= 24.999994 deg-C;   Vel0= 0.0 m/s;   z0= 0.0 m;   }

    State-1: H2O;
    Given:       { p1= 1000.0 kPa;   T1= 400.0 deg-C;   Vel1= 30.0 m/s;   z1= 0.0 m;   A1= 0.0314 m^2;   }
    }

Step 1: Launch the PC Surface State Daemon.

Step 2: Determine State-0 and -1 from the known properties.

Step 3: Use the I/O Panel as a calculator to determine various flow rates.

State-4: Generate the TEST-Code using Super-Calculate. Launch the IG Surface State Daemon on a separate window. Copy the TEST-Code to the I/O Panel of the new daemon and Super-Calculate.

Solution

Launch the Surface State Daemon with the PC model. Evaluate State-1 by entering the given properties. To enter the area you can use the expression '=3.14*(0.1^2)'. The mass flow rate is found as mdot1=3.07 kg/s. Also evaluate State-0, the dead state from p0 and T0 supplied.

To find the flow rate of KE, notice that e=u+ke+pe and pe=0. Therefore, KEdot =mdot1*(e1-u1)=1.38 kW . Similarly, type in '=mdot1*e1', '=mdot1*j1', '=mdot1*s1', '=mdot1*phi1' and '=mdot1*psi1' in the I/O Panel to evaluate the other flow rates as 9087 kW, 10029 kW, 22.94 kW/K, 2357 kW, and 3205 kW. From the flow energy the stream carries, only 3205 kW can be extracted as useful work or exergy.

Now generate the TEST-Code by clicking Super-Calculate button. Also launch the IG Surface State daemon on a separate browser window. Copy the TEST-Code onto the new I/O Panel. Super-Calculate. Evaluate the flow rates on the I/O Panel as follows. The mass flow rate is 3.03 kg/s, very close to the prediction from the PC model. Similarly, the flow rate of kinetic energy is calculated by '=mdot1*(e1-u1)' as 1.36 kW. However, the flow rate of stored and flow energy are calculated as 1288 kW and 2230 kW, almost an order of magnitude smaller than the corresponding PC calculations. This is because the references used for internal energy in the two models are quite different. Entropy also is referenced differently in different models. The exergy on the other hand is based on difference in properties. Therefore the reference values do not influence the values of exergy the same way. The flow rate of flow exergy with the ideal gas model is calculated as 1757 kW. The ideal gas model, although good in predicting the mass flow rate, produces significant error in calculating the flow exergy. This is not attributable to reference values - the ideal gas model simply is not good enough to model steam under the given conditions.

Your input!

For more solved examples on this topic, visit the Slide Show and the Home.TEST.Archive pages. If you detect an error or any inconsistent instructions on this page, or would like to see more examples on a particular topic, please write to me using the Home.Comments page.


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